Study on Deformation Characteristics of the Segment in the Underwater Shield Tunnel with Varying Earth Pressure

Abstract

The segment in an underwater shield tunnel is influenced by the change of earth pressure and water pressure. Therefore, the law of segment deformation should be mastered for the safe operation of the tunnel. To obtain the law of segment deformation under varying earth pressure, loading conditions of constant water pressure and without water pressure were considered. In this study, the numerical simulation and scale model experiment were carried to analyze the strain, curvature, and displacement of the segment. The results show that the strain amplitude of segments is reduced by the water pressure under a range of earth pressure. When the earth pressure ranges from 0 MPa to 2.4 MPa and the water pressure 0.33 MPa, the displacement of the vault and arch waist exhibit a decreased rate of 7.916 mm/MPa and an increased rate of 5.416 mm/MPa, respectively. Under the combined effects of constant water pressure and varying earth pressure, the curvature of the segment tends to stabilize after a rapid change with a maximum of 0.004 m⁻¹.

1. Introduction

In recent years, shield tunneling has been widely used in the construction of underwater tunnels due to its cost-effectiveness and small disturbance to the surrounding soil [1]. However, due to the complexity of the hydrological conditions and geological environment of underwater shield tunnels, there are inevitable phenomena such as crack propagation, deformation accumulation, and resistance attenuation in the tunnel structure, which affect the health status of the shield tunnel segment during the operation stage. It is prone to occur in accidents in tunnel engineering operations [2]. For example, the Kaohsiung Harbor Crossing Submarine Tunnel in Taiwan experienced problems such as structural cracks and water leakage after 20 years of operation. Therefore, it is of great significance to investigate the deformation law of the shield segment for the safety of underwater shield tunnels.

At present, significant achievements have been made in the study of structural deformation of shield tunnels. Feng et al. [3] conducted large-scale model tests based on the Guangzhou Shiziyang Tunnel project to explore the impact of surrounding rock degradation on the mechanical performance of underwater shield tunnel segment structures. Feng et al. [4] conducted experimental and numerical studies on the bending performance of large underwater shield tunnel segment joints. The results showed that the nodes exhibited linear opening and nonlinear deformation after concrete cracking, and the contact surface of the nodes during the opening process was curved. Wang et al. [5] studied the effects of segment joints, segment sizes, and geological conditions on the buckling of shield tunnel lining under hydrostatic pressure through analytical and numerical analysis and concluded that ground support significantly improves the buckling strength, while earth pressure reduces the ability to resist hydrostatic buckling. Ye et al. [6] conducted model tests on three types of segmented ring test models: straight seam ring, staggered seam ring, and uniform ring. They found that the transverse bending stiffness value of the staggered seam assembly ring was significantly greater than that of the straight seam assembly ring, and this difference gradually decreased with the increase of load. Zhang et al. [7] studied the mechanical properties, deformation, stress distribution, crack development process, and failure mode of mining tunnel lining in aquifers under the combined pressure of water and earth through a 1:30 large-scale model test. Under two test conditions, namely only water pressure and variable water pressure but constant earth pressure, cracks and failure occurred successively at the bottom of the wall and the inverted arch.

Yang et al. [8] analyzed the effects of water level changes, seasonal environmental temperature changes, and time effects on tunnel behavior through a multiple linear regression model. The regression results indicate that temperature is the most important factor affecting the strain of the segment during normal operation, and the annual irreversible deformation of the segment joint is as significant as the irreversible deformation caused by changes in water level and temperature. Arnau and Molins [9] used numerical simulations to consider the three-dimensional response generated by local loads and identified the most important influencing parameters and their effects on the response of the lining structure. They pointed out that the stiffness of the surrounding strata determines the degree of interaction between adjacent rings, while the longitudinal compression of the lining determines the maximum load that produces complete interaction. Cheng et al. [10] investigated the influence of excavation depth ratio and unloading ratio on tunnel displacement behavior through a series of numerical simulations and concluded that the axial force at or near the tunnel sidewall is the most sensitive to the unloading effect caused by excavation activities. Liu et al. [11] designed and implemented a full-scale test on the bearing capacity of staggered assembled shield tunnel structures based on unloading conditions. Under the design load, the progressive failure and ultimate bearing capacity of the staggered segment lining were obtained. Based on considering the elastic-plastic properties of bolts and concrete, Cheng et al. [12] provided analytical solutions for the longitudinal equivalent bending stiffness and shear stiffness of circumferential nodes and proposed two shear load transfer theoretical models for the arrangement of circumferential nodes. Zhang et al. [13] conducted a series of full-scale experimental studies on the failure characteristics of the key segment in super-large cross-section shield tunnels under general loads. The results showed that the longitudinal force acting along the tunnel axis significantly limits the inward convergence of the segment, the opening of circumferential seams, and the displacement of longitudinal and circumferential seams within a certain range. Zhang et al. [14] compared and analyzed the characteristics of structural instability and failure of two types of segment structures under high water pressure through prototype tests of straight seam assembly structure and staggered seam assembly structure segment in the Shiziyang Tunnel. Deng et al. [15] pointed out that concrete structures operating in a water environment for extended periods are in a state of long-term water saturation. The free water present in the concrete pores exerts a certain water pressure on the pore walls under various loads, thereby affecting the static strength of the concrete. Yang et al. [16] studied the effect characteristics of concrete under different water-confining pressures after cyclic loading. Sheng et al. [17] summarized that the concrete structure operating in the water environment exhibits different damage laws and mechanisms under dynamic loading due to the influence of free water. Therefore, it is of great significance to the study of the mechanical characteristics of underwater shield tunnel structures.

From this, it can be seen that the structural deformation and settlement laws of shield tunnels under the influence of a single factor of water pressure or earth pressure are clear. However, under the combined action of water pressure and formation pressure, the stress on the segment structure is indeterminate, and the deformation mechanism is complex. The structural deformation law is not yet clear under the conditions of dual factor cross fusion, especially under the influence of constant water pressure and earth changes pressure. Previous studies often used single physical quantities such as displacement and strain to describe deformation results, which made it difficult to accurately reflect the deformation state of the tunnel segment. Based on this, to make the test conclusion more accurate, the results of the scale test and numerical simulation should be used to verify each other. Firstly, in Section 2.1, the design of numerical simulation parameters is introduced, as well as the setting of measuring points and working conditions. Subsequently, in Section 2.2, the preparation and test scheme for the scale test materials are detailed. In order to obtain the deformation characteristics of underwater shield tunnel segments, in Section 3, the structural strain, curvature, and displacement of the shield tunnel segments under different earth pressures, in both conditions with and without water pressure, were compared and analyzed through numerical simulation and scale model experiments. In Section 4, the deformation characteristics of the shield tunnel segment under the combined action of water pressure and earth pressure are summarized, which provides a reference for the health monitoring, damage prediction, and disaster warning threshold setting of underwater shield tunnels. In addition, this study can provide guiding significance for selecting the appropriate tunnel burial depth in the stratum environment with little difference in water pressure in the planning of the shield tunnel.

2. Numerical Simulation and Scale Model Experiment

2.1. Numerical Simulation of Underwater Shield Tunnels

2.1.1. Model Dimensions and Boundary Conditions

Based on the Jinan Yellow River Shield Tunnel, a shield tunnel segment model was established in ANSYS 16.0. The stratum that the shield tunnel passes through is mainly silty clay, locally with calcareous nodules and lens-shaped fine sand and medium sand strata. The lining rings are 15.2 m in outer diameter, 13.9 m in inner diameter, 0.65 m thick, and 2.0 m wide. C60 reinforced concrete is used.

Taking the longitudinal direction of the tunnel as the Z-axis and the vertical direction as the Y-axis, the Y-axis is rotated 90 degrees clockwise to obtain the X-axis. The boundary dimensions of the numerical model are X × Y × Z = 90 × 84 × 10 m. Three-dimensional static analysis was conducted to simulate the deformation of the shield tunnel segment during operation. The Mohr–Coulomb [18] constitutive model was used for the geological layer, and a homogeneous elastic body model was used for the lining. The tunnel segment was treated as a whole, made of C60 reinforced concrete with a thickness of 80 cm. SOLID185 solid elements were used to construct the tunnel support and the surrounding rock. Detailed calculation parameters for the surrounding rock and lining structure are listed in

Table 1. Calculation parameters of surrounding rock and supporting structure.

Calculation Parameters	Severe	Modulus of Elasticity	Poisson’s Ratio	The Angle of Internal Friction	Cohesion
	γ (kN/m3)	E (GPa)	μ	φ (°)	C (MPa)
Stratum	19	0.045	0.33	20	38
Segment	23.6	36	0.2	/	/

.

The contact unit was constructed on the contact surface between the segment structure and the stratum structure to simulate the friction effect between the shield tunnel segment and the stratum. The ANSYS APDL 16.0 classical interface is used to apply the contact element, where the inner surface of the stratum is set as the target surface, and the outer surface of the segment is designated as the contact surface. The contact element’s interaction model selects the binding contact, ensuring that the segment and the stratum remain in constant contact. Additionally, the normal contact relation algorithm employs the extended Lagrange multiplier method to achieve a realistic contact condition with zero penetration. On this basis, ensuring that the two models do not penetrate each other under the force condition. The interaction model of the contact unit was chosen to bind the contact so that the segment was always in contact with the formation. Meanwhile, the normal contact relationship algorithm was chosen to extend the Lagrange multiplier method to achieve a real contact condition where the penetration was zero. The friction coefficient between contact elements was set to the actual geological friction coefficient, which is 0.4.

The segment and formation model has lateral constraints on the four faces of X = 0, vertical constraints on the four faces of Y = 0, and vertical constraints on the faces of Z = 0 and Z = −4. The ground surface was set as a free boundary, and the lateral stress was determined by the lateral pressure coefficient.

2.1.2. Measuring Point Layout and Working Condition Setting

To analyze the structural deformation of the shield tunnel segment under the cross-section of water pressure and earth pressure. The tunnel cross-section with a longitudinal distance of 5 m was taken as the measuring section. The measuring target was the inner surface of the segment. The structural deformation measuring points were set at intervals of 18 degrees of arc angle, and 20 measuring points were set in total. In the subsequent analysis, the points from the above parts will be used, which are distinguished by different color markers, as shown in Figure 1.

According to the maximum water level of 33.09 m based on practical engineering and the permeability of the covered soil of the tunnel was micro-permeable or weakly permeable. The experiment applied uniformly distributed water pressure (0.33 MPa) and earth pressure (vertical load range of 0.4–2.4 MPa) sequentially. The lateral pressure coefficient of earth pressure was 0.5, and the earth pressure was gradually loaded from 0 MPa to 2.4 MPa with a gradient of 0.4 MPa. 0.33 MPa uniformly distributed water pressure is used to simulate the maximum water level of 33.09 m in the actual project. Earth pressures of 0.4 MPa and 0.8 MPa, respectively, correspond to the minimum overburden thicknesses of 25 m and maximum overburden thicknesses of 38 m.

2.2. Scale Model Experiment of Underwater Shield Tunnels

2.2.1. Similar Relationship

Considering the reliability, economy, and flexibility of the model experiment, the geometric similarity ratio of 1:20 and the gravity similarity ratio of 1:1 was selected for the model experiment. According to the three similarity theorems, the similarity relationship of relevant physical and mechanical quantities is determined. The similarity ratio of Poisson’s ratio, strain, and friction angle: $C_u=C_{\epsilon }=C_{\phi }=1$; the similarity ratio of strength, stress, elastic modulus, and displacement: $C_R=C_{\sigma }=C_E=C_{\delta }=20$.

2.2.2. Preparation of Similar Materials

(1)

Segment Model Fabrication

According to the similar ratio mentioned above, a segment model was made with a fixed water-to-gypsum ratio of 1:1.4. The total height of the model is 20 cm (ring height 10 cm, half-ring height 5 cm), the outer diameter is 0.38 m, and the inner diameter is 0.35 m.

After the main body of the shield tunnel segment model is completed, we will conduct a segment joint simulation. For the longitudinal joint form of the segment, the segment joint was simulated through slotting [19], and a slotted joint of a certain depth was opened in the part of the model ring corresponding to the tunnel joint to weaken the flexural stiffness of this part, as shown in Figure 2. The depth of the slotted joints was arranged according to the equivalence principle of unequal positive and negative flexural stiffnesses with the prototype joint. For the segment ring joint form, bolts with a diameter of 4 mm and a length of 20 mm were inserted longitudinally from the tunnel into the inside of the model at the corresponding ring joint position on the model, as shown in Figure 2. The segment rings were spliced, and the shear stiffness between the structural rings is regarded as infinite.

(2)

Formation Material Preparation

The experiment’s geometric similarity ratio of 1:20 was taken as the basic similarity ratio for the formation of similar material. Based on the research on similar material [20], the mixture of barite powder, fly ash, engine oil, and river sand was used to simulate the prototype formation. The control parameters of the model soil are elastic modulus E, bulk density γ, internal friction angle φ, and cohesion c. The control parameters of the model soil can be calculated according to the similarity ratio, as shown in

Table 2. Similarity parameters of model experiment soil.

Mechanical Parameter	Severe γ	Modulus of Elasticity E	Cohesive Force c	Internal Friction Angle
	(kN/m3)	(MPa)	(MPa)	φ (°)
Prototype soil	19	45	38	20
Model soil	19	2.25	1.95	20

.

According to the model soil parameters described in Table 2, combined with the study of a similar stratum model of a shield [21], the weight ratios of barite powder, fly ash, engine oil, and river sand were determined to be 0.25, 0.225, 0.125, and 0.4, respectively.

2.2.3. Test Apparatus

(1)

Experiment Device

This experiment required water loading and surrounding rock pressure loading on the segment model. The shield tunnel-stratum similar model test system was used to simulate the surrounding rock pressure loading, as shown in Figure 3. The water pressure loading device was used to simulate the water loading. It mainly consisted of two symmetrically placed water adjustment devices and eight steel strands. By applying torque to the eight steel strands through the adjustment devices, the steel strands were tightened around the segment ring. The water pressure value was confirmed using the tension gauge on the left, and finally, the steel strands were fixed by bolts on the adjustment devices to stabilize the ring towards the water pressure value.

Due to the advantages of high precision, good stability, high sensitivity, and convenient use, fiber grating is often introduced into shield tunnel deformation measuring [22,23]. To collect the deformation information of the segment model under the combined action of water pressure and surrounding rock pressure, fiber Bragg grating (FBG) was used as a deformation measuring sensor. Select the middle section of the segment model complete ring as the structure deformation sensing object, and evenly arrange FBG sensors on the inner surface of the segment in the circumferential direction. In the similarity relationship, the similarity ratio of the angle is 1:1, ensuring that the arrangement of measuring points in the scale test aligns with that in the simulation test. The length of the elements was selected as 8 cm. The structural deformation measuring points were set at intervals of 18 degrees of arc angle, and 20 FBG sensors were arranged in the circumferential direction, as shown in Figure 1.

(2)

Loading Scheme

Place the shield tunnel segment model with the pasted FBG sensing element on the experiment platform, fill the outer gap of the segment model with prepared similar soil, and compact it to fix the model. Radial, vertical, and lateral loads of the segment model were applied by jacks located above the platform and in front, back, left, and right positions.

(3)

Experimental Conditions

Based on the maximum water pressure of the actual project and the similarity relationship, the test water pressure is 0.322 MPa. The coefficient of lateral pressure was selected as 0.5. Surrounding rock pressures were applied to the model in three directions, as shown in Figure 3. The vertical surrounding rock pressure of the tunnel was gradually loaded from 0.4 MPa to 6.0 MPa with an increment of 0.4 MPa. The lateral surrounding rock pressure of the tunnel was gradually loaded from 0.2 MPa to 3.0 MPa with an increment of 0.2 MPa. The radial surrounding rock pressure of the tunnel only ensured that there was no radial deformation between the segment and soil, so the radial surrounding rock pressure was maintained at 16.0 MPa. After each level of surrounding rock pressure was loaded, a stable pressure state was maintained for 5 min to record the deformation data of the segment.

3. Results and Discussion

When the surrounding rock pressure reaches 3.6 MPa as applied by the loading device, the similar soil becomes completely compacted, and at this time, the load was fully applied to the surface of the segment model.

To compare and verify the results between the model experiment and numerical simulation, we took the complete earth pressure that the segment was subjected to when the surrounding rock pressure was loaded to 3.6 MPa as the real load of the segment with 0.0 MPa in numerical simulation. The segment is in a deformed state under load in the range of 4.0 to 6.0 MPa, corresponding to a real load on the segment in the range of 0.4 to 2.4 MPa in numerical simulation.

3.1. The Strain of the Segment

Based on the numerical simulation results, the deformation of the tunnel segment structure exhibits obvious characteristics within the loading range from 0 to 2.4 MPa. Especially under the earth pressures of 0.4 MPa and 0.8 MPa, the difference in the effect of water pressure on the deformation of the segment is more significant. Starting from the right arch waist (No. 6), the strain values of each point are plotted in the diagram, following a counterclockwise direction of Figure 1 as the standard. The related deformation characteristics are shown in Figure 4.

Under the condition of earth pressure, the strain of the segment with water pressure is larger than that without water pressure, and the strain difference of the arch crown is 10.0 με, and that of the arch waist is 12 με under 0.4 MPa load. Under the load of 0.8 MPa, the strain difference of the arch crown is 27.6 με, and that of the arch waist is 141.4 με. However, the strain difference of the segment at each measuring point is relatively stable under 0.4 MPa and fluctuates greatly under 0.8 MPa.

According to the analysis above, it can be concluded that the uniform water pressure of 0.33 MPa results in stable strain variation of the segment under a vertical earth pressure of 0.4 MPa, which is beneficial to the stability of the segment structure. However, under an earth pressure of 0.8 MPa, the strain fluctuates greatly, and the advantageous effect of water pressure after this load is reduced. That is, the uniform water pressure of 0.33 MPa has an effective stabilizing effect on the strain of the segment under a vertical load of 0.4 MPa, avoiding structural damage caused by large strain fluctuations of the segment.

Due to the symmetrical deformation of the segment, in this study, the strain information of the 1/4 ring segment under different earth pressures was taken to analyze the deformation characteristics and strain features of the segment under the combined action of uniform water pressure and earth pressure. The load–strain curve is shown in Figure 5. The tensile strain occurred at the crown, right shoulder 2 and 3 measurement points of the segment, while the compressive strain occurred at the right shoulder 4, 5 and the crown waist measurement points and the strain on the inner surface of the segment continuously increased with the increase of earth pressure. After applying water pressure to the segment, the strain growth rate between various measurement points increased unevenly with the increase of earth pressure, exhibiting a fluctuating trend. Subsequently, the shield tunnel segment experiences a brief and gradual decrease in strain within the loading range. The arch compression strain of the segment decreases from −376.0 με to −344.0 με, occurring in the range of 0.8–1.2 MPa, as shown earlier in Figure 4. While the crown tension strain of the segment decreases from 126.4 με to 84.6 με, occurring in the range of 1.2–1.6 MPa, as shown in the “late” in Figure 4. After the appearance of a slow decrease in the strain at each measurement point on the segment, the strain continues to increase at a growth rate of 21–35% with the increasing earth pressure.

Therefore, the variations in tensile strain and compressive strain for the segment are not synchronous under the combined action of water pressure and earth pressure. The phenomenon of strain reduction at the arch waist position appears earlier than that at the vault position. Combined with the material characteristics of reinforced concrete, it can be known that the tensile strength of concrete is small, and the tensile side is more prone to crack damage. Therefore, the phenomenon of strain reduction at the arch waist position can be taken as the threshold starting point of a large tensile strain of the segment structure, which will be beneficial to the deformation monitoring and early warning of the underwater shield tunnel segment.

The strain results of the model experiment are shown in Figure 6. It can be seen from Figure 6 that, with a uniformly distributed water pressure of 322 N applied, the maximum tensile strain on the inner surface of the segment model is 43.56 με (at measurement point 17) and the maximum compressive strain on the surface is 47.68 με (at measurement point 7). When the experimental loading device loaded the stratum load of 3.6 MPa, the strain distribution of the segment model showed a more significant change. The maximum compressive strain of the segment was −74.63 με, and the maximum tensile strain was 18.41 με. When the stratum load was 4.0 MPa, the maximum compressive strain of the segment was −177.38 με, and the maximum tensile strain was 86.23 με. When the stratum load was 4.4 MPa, the maximum compressive strain of the segment was −320.81 με, and the maximum tensile strain was 144.38 με. With the increase of the stratum load, the strain distribution of the segment model showed a significant increase in amplitude change. The strain on both sides of the segment arch waist shifted inward, and the offset gradually increased. The strain at the top and waist of the segment shifted outward, and the offset gradually increased. When the earth pressure increases to 5.6 MPa, there were significant numerical changes in the strain distribution of the segment model, which were caused by the material properties of the model itself and the development of internal cracks. At this point, penetrating cracks had appeared in the segment model, resulting in the failure and destruction of the model.

The strain distribution map of the segment model reveals that the structural strain of the segment increases continuously during the loading process of the surrounding rock pressure. Specifically, tensile strain occurs in the interval between the arch top and arch bottom, while compressive strain takes place within the intervals of the left and right arch waist. The real-time deformation of the segment model exhibits a characteristic feature of inward convergence at the arch top and arch bottom, and outward protrusion at the left and right arch waist.

In summary, two identical conclusions were obtained by comparing the numerical simulation results under the action of water–earth pressure. One is that the strain of the model experiment segment is not synchronized; the strain reduction around the arch waist occurs earlier than around the arch crown. Another is that when the segment structure is subjected to the pressure of the surrounding rock, the tensile strain at the arch top and arch bottom gradually increases, and the structure of the arch top and arch bottom contracts and deforms inward. The compressive strain of the arch waist gradually increases, and the arch waist structures on both sides protrude outward and deform.

3.2. The Curvature of the Segment

In numerical simulations, due to the segment being a homogeneous circular ring, its deformation presents a symmetrical form, and the structural deformation is more likely to occur at the crown and haunch locations of the segment. Therefore, the curvature changes data of the two measurement point locations: the crown and haunch of the segment were selected for analysis. To facilitate data acquisition and calculation of the curvature data, it was assumed that the measurement points and adjacent nodes are on the same circular arc line when calculating the curvature data. The curvature changes curves of the crown and haunch measurement points of the segment under two water pressure conditions are shown in Figure 7.

Regardless of the presence of water pressure, as the soil pressure increases, the curvature of the crown continuously decreases, while the curvature of the segment waist continuously increases. It can be seen from Figure 7 that when the vertical soil pressure is from 0.4 to 1.2 MPa, the curvature undergoes a rapid increase and decrease stage; when the vertical soil pressure is between 1.2 and 2.4 MPa, the curvature undergoes a slow increase and decrease stage. During the vertical soil pressure of between 1.2 and 2.4 MPa, when there is water pressure, the average rate of change in curvature of the arch crown is 32%, while without water pressure, it is 35%. Regardless of whether there is water pressure or not, the average rate of change in curvature of the arch waist is 39%. During the slow increase and decrease stage of curvature, without water pressure, the average rate of change in curvature of both the arch crown and arch waist is 13%, and with water pressure, the variation range of the curvature of the arch crown and arch waist tends to be close to 0.

In summary, under both conditions of water pressure and no water pressure, the curvature variation of the segment shows a similar changing trend but exhibits different characteristics. Specifically, firstly, without water pressure, the curvature of the arch crown and arch waist positions of the segment exhibit linear changing characteristics. That is, the curvature at the arch crown position first increases rapidly and then gradually increases linearly, while at the arch waist position, the curvature first decreases rapidly and then gradually decreases linearly. Secondly, with water pressure, the curvature at the arch crown position of the segment first increases at a slower speed then increases rapidly, and finally tends to be stable; while the curvature at the arch waist position first decreases at a slower speed, then decreases rapidly, and eventually stabilizes. Thirdly, in the vertical earth pressure range from 0.4 to 1.2 MPa, the amplitude of curvature variation of both the arch crown and arch waist is the same, while in the vertical earth pressure range between 1.2 and 2.4 MPa, the curvature variation amplitude of both the arch crown and arch waist of the segment decrease when there is water pressure.

Regarding the analysis of the model experiment results, since the crown is a common location of deformation in engineering, the curvature of the key position measurement points of the segmental lining model, namely the crown, was selected as an example crown to analyze the deformation law of the shield tunnel segmental lining structure. The load–curvature variation curve of the crown measurement point of the segmental lining model is shown in Figure 8.

In Figure 8, the curvature of measuring point 1 at the arch crown of the shield tunnel segment model sharply increases (with a maximum slope of 0.3) in the load range of 3.6 to 4.4 MPa until the vertical soil pressure reaches 4.4 MPa and a crack pass through, causing the release of structural stress and leading to a sudden drop in the curvature at the arch crown. At the same time, with the development of crack penetration and secondary cracks, the bearing capacity of the segment gradually decreases, and the curvature decreases gradually. Combined with the strain analysis, it can be seen that the curvature can accurately reflect the structural deformation state information of the segment model, and it can be considered that when the curvature increases sharply, cracks may appear in the shield segment.

3.3. The Displacement of the Segment

Through numerical simulation calculation, the displacement change data of segment characteristic position under water pressure and no water pressure are obtained, as shown in Figure 9. Whether water pressure exists or not, the displacement of the vault is larger than that of the arch waist in the whole range of earth pressure, which accords with the deformation law of the tunnel structure. However, the existence of water pressure on the deformation of the segment produced a disturbance, making the segment displacement change. When the shield tunnel is only subjected to earth pressure, the displacement of the segment vault and arch waist is linear with the earth pressure, the displacement of the vault increases with the growth rate of −7.77 mm/MPa, and the displacement of the arch waist increases with the growth rate of 5.51 mm/MPa. When the shield tunnel is subjected to uniform water pressure and earth pressure, the displacement of the vault and the arch waist of the segment fluctuate in the range of 0.4~1.6 MPa earth pressure. When the earth pressure exceeds 1.6 MPa, the displacement of the segment is linear with the earth pressure. The increase rate of the vault displacement is −7.45 mm/MPa, and the displacement of the arch waist is 5.23 mm/MPa. It can be seen that the load-displacement curve at this time is very close to the displacement curve without water pressure.

According to the characteristics of strain variation of the segment, it can be concluded that the displacement of the segment will be disturbed by uniform water pressure, and the deformation fluctuation of the segment will occur under small earth pressure (the displacement decreases with the increased load). Because the displacement fluctuation phenomenon only occurs in the load range where the earth pressure is less than 1.6 MPa, it can be considered that the displacement fluctuation phenomenon caused by water pressure only exists in the small, buried depth (earth pressure is less than 1.6 MPa). Similarly, when the embedded depth of the shield tunnel segment is large (the earth pressure is greater than 1.6 MPa), it can be considered that the displacement of the segment increases linearly with the earth pressure.

For the model experiment results, the displacement data at the key locations of the tunnel were taken to draw displacement curves, as shown in Figure 10. Since the displacement gauges were installed after loading water pressure, the state of the segment after loading water pressure was considered as the initial state of displacement, and the displacement was zero.

It can be seen from Figure 10 that the shield tunnel segment vault (measuring point 1) and the vault bottom (measuring point 11) both produce inward shrinkage deformation, and the left and right arch waist positions both produce outward expansion deformation. In the load range from 3.6 to 4.0 MPa, the deformation of the segment lining is small and only changes slowly within 0.5 mm. During loading, the arch crown and right arch waist show a trend of inward displacement, while the arch foot and left arch waist show a trend of outward expansion displacement. In the load range from 4.0 to 5.2 MPa, the displacement shows a fluctuating trend. Combined with the displacement results of numerical simulation under the load range from 0 to 0.4 MPa (corresponding to the load range of the model experiment from 3.6 to 4.0 MPa), it can be seen that the uniformly distributed water pressure acting on the segment lining is beneficial for the segment to withstand a certain range of soil pressure. Under the combined action of uniformly distributed water pressure and smaller earth pressure (load range from 3.6 to 4.0 MPa), the segment undergoes asymmetric deformation, with the arch crown and right arch waist (right shoulder area) exhibiting inward contraction deformation, and the arch foot and left arch waist (left shoulder area) exhibiting outward expansion deformation. When uniformly distributed water pressure and larger earth pressure (load range from 4.0 to 6.0 MPa) act together, the strengthening effect produced by water pressure is counteracted by earth pressure, and the deformation of the segment becomes symmetric, with the arch crown and arch foot showing inward displacement and the arch waist showing outward displacement.

4. Conclusions

In this study, the deformation of the shield tunnel segment under two conditions with and without water was numerically simulated with ANSYS 16.0. To verify the numerical simulation results, a 1:20 scale model experiment was conducted using a shield tunnel-geological composite system simulation experiment system to obtain information on the deformation of the segment. The deformation characteristics of the shield tunnel segment underwater were explored from structural strain, curvature, and displacement perspectives by comparing and verifying the numerical simulation and model experiment results. The conclusions are as follows:

(1)

A uniformly distributed water pressure of 0.33 MPa had a stabilizing effect on the segment strain under a vertical load of 0.4 MPa under the combined action of water and soil pressure. However, the effect was counteracted after reaching 0.4 MPa. The strain at the arch crown and arch waist gradually increased with the increase in load. Both numerical simulation and model experiment results, in a specific load range (numerical simulation from 1.2 to 1.6 MPa, corresponding to model experiment from 4.8 to 5.2 MPa), showed a sudden decrease followed by the rapid increase in strain at the arch crown. In the model experiment, there was no strain mutation phenomenon at the arch waist, but it showed a continuously increasing trend.

(2)

The curvature of the shield tunnel segment changes linearly in the stratum without water pressure. The curvature amplitude of the segment decreases in the stratum as water pressure.

(3)

In the stratum with water pressure, the displacement of the segment fluctuates in the range of 0–1.6 MPa (corresponding to 3.6–5.2 MPa in the model experiment), while in the range of 1.6–2.4 MPa (corresponding to 5.2–6.0 MPa in the model experiment. The segment has cracks), the displacement of the segment presents linear change.

(4)

Before the appearance of the cracks in the scale model, the displacement of the tunnel segment steadily increases. There are significant fluctuations in the values of strain and curvature when cracks occur, while displacement remains unchanged. The combination of strain, curvature, and displacement of the shield tunnel segment structure can well reflect the structural deformation information.